Question

There are 351 children in a school. There are 7 boys to every 6 girls. How many boys are there? How many girls are there?

Answer 1

Hint: To find the total number of boys and girls in the school use the concept of ratio and proportion. Let the total number of boys be $b$. Since there is one ratio of boys is 7 out of 13 and similarly another proportion of boys to total strength is $b$ out of 351 . Equate both the proportion and find the value of $b$ i.e. number of boys. Subtract value of $b$ from total of 351 to get the number of girls .

Complete step by step solution:
According to the question we are given that there are a total 351 children in a school in which there are 7 boys to every 6 girls.
In other words we can also say that the ratio of boys to girls in the schools is 7 to 6. So we can say that 7 out of every 13 children are boys and on the other hand 6 out of every 13 students are girls .
Let the total number of boys in the school be $b$.
Trying to set up a proportion for the number of boys, we get
$ \Rightarrow \dfrac{7}{{13}} = \dfrac{b}{{351}}$
Cross multiplying the terms , we get
\[
   \Rightarrow 7 \times 351 = 13 \times b \\
   \Rightarrow 13b = 7 \times 351 \\
]
Dividing both sides of the equation with the coefficient of $b$ i.e. $13$, we get the value of $b$ as
\
[ \Rightarrow \dfrac{{13b}}{{13}} = \dfrac{{7 \times 351}}{{13}}\]
Simplifying further, we get
\[ \Rightarrow b = 189\]
Hence the number of boys in school of strength $351$ is equal to $189$.
So the number of girls in schools will be
Total girls = total children - {total boys}
Total girls= 351 - 189
Total girls= 162
Alternate:
Alternatively, you can obtain the number of boys and girls using algebra by finding the proportionality constant.
Let the proportionality constant be $x$. Since the total number given by the ratio is equal to 13.
So, 13 multiplied by the proportionality constant is the total number of children.
$
  13x = 351 \\
  x = \dfrac{{351}}{{13}} \\
  x = 27 \\
 $
Total number of boys $ = 7x = 7\left( {27} \right) = 189$
Total number of boys $ = 6x = 6\left( {27} \right) = 162$
Total children $ = 189 + 162 = 351$

Therefore, the total number of girls and boys in school of strength $351$ are $162$ and $189$ respectively.

Note: Mathematical equation : A Mathematical equation can be defined as the mathematical statement which contain an equal symbol $ = $ in between two algebraic expressions that share the same value
1. Read the statement carefully in order to convert them into mathematical expressions.
2. You can also set the proportion for girls by assuming the total girls as $g$ and proportion as $\dfrac{6}{{13}} = \dfrac{g}{{351}}$. The answer will be the same.
3. Don’t confuse with the proportions and ratios